%TEST8 test cs_cholsol, cs_lusol
%
% Example:
%   test8
% See also: testall

%   Copyright 2006-2007, Timothy A. Davis.
%   http://www.cise.ufl.edu/research/sparse

index = UFget ;
[ignore f] = sort (max (index.nrows, index.ncols)) ;
f = f (1:100) ;

% f = f(1)

for i = f
    Prob = UFget (i) ;
    disp (Prob) ;
    A = Prob.A ;
    [m n] = size (A) ;
    if (~isreal (A) | m ~= n)						    %#ok
	continue
    end

    spd = 0 ;
    if (m == n)
	if (nnz (A-A') == 0)
	    try
		p = amd (A) ;
	    catch
		p = symamd (A) ;
	    end
	    [R,p] = chol (A (p,p)) ;
	    spd = (p == 0) ;
	end
    end

    if (spd)
	C = A ;
    else
	C = A*A' + n*speye (n) ;
	try
	    p = amd (C) ;
	catch
	    p = symamd (C) ;
	end
	try
	    R = chol (C (p,p)) ;
	catch
	    continue
	end
    end

    b = rand (n,1) ;

    x1 = C\b ;
    x2 = cs_cholsol (C,b) ;
    r1 = norm (C*x1-b,1) / norm (C,1) ;
    r2 = norm (C*x2-b,1) / norm (C,1) ;
    err = abs (r1-r2) ;
    fprintf ('err %g\n', err) ;
    if (err > 1e-10)
	error ('!') ;
    end

    x2 = cs_lusol (C,b, 1, 0.001) ;
    r2 = norm (C*x2-b,1) / norm (C,1) ;
    err = abs (r1-r2) ;
    fprintf ('err %g (lu with amd(A+A'')\n', err) ;
    if (err > 1e-10)
	error ('!') ;
    end

    if (m ~= n)
	continue ;
    end

    x1 = A\b ;
    r1 = norm (A*x1-b,1) / norm (A,1) ;
    if (r1 < 1e-6)
	x2 = cs_lusol (A,b) ;
	r2 = norm (A*x2-b,1) / norm (A,1) ;
	fprintf ('lu resid %g %g\n', r1, r2) ;
    end
end
